Test Index

Probability

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Question : 98 of 127

Marks: +1, -0

A husband and his wife appear in an interview for two vacancies. The probability of their selection are respectively

\frac{1}{4}

\frac{1}{3}.

What is the probability that only one of them will be selected?

$\frac{5}{11}$
$\frac{5}{12}$
$\frac{5}{13}$
$\frac{5}{14}$

Solution:

Concept:

Find the probability that exactly one of them is selected using independence.

Explanation:

Let

P(H) = \frac{1}{4}

be the probability husband is selected.

Let

P(W) = \frac{1}{3}

be the probability wife is selected.

Assume selections are independent.

Then

P(\text{only one}) = P(H \text{ and not } W) + P(\text{not } H \text{ and } W)

.

P(\text{not } H) = 1 - \frac{1}{4} = \frac{3}{4}

.

P(\text{not } W) = 1 - \frac{1}{3} = \frac{2}{3}

.

So

P(\text{only one}) = \frac{1}{4} \times \frac{2}{3} + \frac{3}{4} \times \frac{1}{3} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12}

.

Answer:

\frac{5}{12}

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